1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Error Propagation - Estimating Variance

  1. Oct 29, 2013 #1
    1. The problem statement, all variables and given/known data

    Not exactly a homework question, but rather a section in Statistical Data Analysis:

    Suppose there is a pdf y(x)[/SUB] that is not completely known, but μi and Vij are known:

    2. Relevant equations

    3. The attempt at a solution

    I understand how <y(x)> ≈ y(μ),

    My confusion:

    Why does <y(x2)>

    1. Imply we square everything throughout?

    <[y(μ) + Ʃ[∂y/∂x](xi - μi)]2>

    2. give a xi and xj term? Where did the xj come from?

    3. Why is it for i≠j when xi and xj are uncorrelated, the expression simplifies to

    σ2y ≈ Ʃ[∂y/∂x]2σ2i

    Where did the j go?

    Last edited: Oct 29, 2013
  2. jcsd
  3. Oct 30, 2013 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    It told you explicitly where the j "went": it said that ##V_{ii} = \sigma_i^2## and that ##V_{ij} = 0 ## for ##i \neq j##.
  4. Oct 31, 2013 #3
    Hmm, that makes sense.

    What about the initial derivation? Why did they choose to square the entire RHS when it's a function of (x2) and not f2(x)? And the j's started appearing..
  5. Oct 31, 2013 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Do you honestly mean to say that you cannot tell the difference between ##g(x)^2## and ##g(x^2)##? The paper is working with ##g(x)^2##!
  6. Oct 31, 2013 #5
    Ah I see, but where did the j's come from though? And nothing about y(x2) was said that day.
  7. Oct 31, 2013 #6

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Try it for yourself: write out ##(\sum_{i=1}^3 a_i)^2 = (a_1 + a_2 + a_3)^2## in complete detail, by expanding out the square. After doing that, re-write the result using summation notation.

    This will be my last post on this topic.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted